In a known apparatus of this type for detachably fastening a cable under tension (German Pat. No. 1,266,384), a clamping unit pressed by a coil spring against the tapering end of the sleeve is held in a thick-walled sleeve having an inner hole in such a way that the said clamping unit is axially displaceable and so that this unit is self-locking and clamps in the hole a cable inserted into the sleeve via an end orifice. The coil spring tapers conically towards the clamping unit. The sleeve is provided with a further hole for easy insertion and tensioning of the cable in an advantageous oblique position with respect to the inner hole, and furthermore a lever projecting through the sleeve serves for operation of the clamping unit. This lever consists of an angled wire section which engages a backward projection of the clamping unit. Since this clamping unit, which has a circular or semicircular cross-section, is matched to the hole, which is likewise circular, this lever generally ensures sufficient guidance of the clamping unit. However, a circular clamping unit has the disadvantage that it comes into contact with the rope to be clamped only with its relatively small peripheral curvature and the spring pressure in this case may be sufficient for secure clamping. On the other hand, a readily deformable rope may in turn be clamped so strongly that it is very difficult to release from this clamping position using the known lever. In another apparatus for detachably fastening a cable (German Pat. No. 1,302,092), the clamping unit is a roller which has a knurled circumference and sits in a displaceable bearing part which can be moved by means of a handle. The hole is shaped like the clamping unit in order to hold the latter. The coil spring engages the displaceable bearing part. Although the roller substantially prevents disadvantageous clamping positions, unclamping cannot always be effected rapidly and without particular force, even with the known handle.